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The action for a 5-brane to a string

  1. Feb 22, 2013 #1
    Given an action for a 5-brance
    ##S=\int d^6x\left[\sqrt{-g}{1\over
    {4\partial_r a\partial^r a}}\partial_ma(x)F^{*mnl}F_{nlp}\partial^pa(x)+
    \sqrt{-\det(g_{mn}+i\tilde F_{mn})}\right],##
    where ##x^m## ##(m=0,1...,5)## are local coordinates of the worldvolume, ##g_{mn}(x)=\partial_mX^M(x)g_{MN}\partial_nX^N(x)## is a worldvolume metric
    induced by embedding into curved target space with the metric ##g_{MN}(X)## parametrized by coordinates ##X^M## ##(M,N=0,...,D-1)##; ##F_{mnl}=2(\partial_{l}A_{mn}+ \partial_{m}A_{nl}+\partial_{n}A_{lm})## is the field strength of an antisymmetric worldvolume gauge field ##A_{mn}(x)##;
    ##g=\det{g_{mn}}##; ##F^{*lmn}## is the dual field strength:
    $$ F^{*lmn}={1\over {6\sqrt{-g}}} \varepsilon^{lmnpqr}F_{pqr} $$
    and
    $$\tilde
    F_{mn}\equiv{1\over{\sqrt{(\partial a)^2}}}F^{*}_{mnl}\partial^la(x).$$

    The scalar field ##a(x)## ensures manifest ##d=6## covariance of the model and is completely auxiliary.

    My question is how do I reduce it to a 1-brance, i.e., a string?
    Is there any standard procedure for this kind of problem?

    Any devices would be very appreciated.
     
  2. jcsd
  3. Feb 26, 2013 #2
    A string comes from compactifying an M-theory 2-brane on a circle. The M-theory 5-brane doesn't become a string, it becomes a D5-brane (or D4-brane) or a "heterotic fivebrane". Although the 5-brane and the 2-brane are related, and there may be some compactification where a wrapped 5-brane is dual to a string.
     
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